Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-6x+3y &= -6 \\ 9x-9y &= 3\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-9y = -9x+3$ Divide both sides by $-9$ to isolate $y$ $y = {x - \dfrac{1}{3}}$ Substitute this expression for $y$ in the first equation. $-6x+3({x - \dfrac{1}{3}}) = -6$ $-6x + 3x - 1 = -6$ Simplify by combining terms, then solve for $x$ $-3x - 1 = -6$ $-3x = -5$ $x = \dfrac{5}{3}$ Substitute $\dfrac{5}{3}$ for $x$ back into the top equation. $-6( \dfrac{5}{3})+3y = -6$ $-10+3y = -6$ $3y = 4$ $y = \dfrac{4}{3}$ The solution is $\enspace x = \dfrac{5}{3}, \enspace y = \dfrac{4}{3}$.